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\begin{document}
\title{Lab 2: Source Measurement}
\author{Alexandra Booth \and Glenn Sweeney}

% make the title area
\maketitle

% make introduction
\section{Introduction}

A spectroradiometer is a specialized tool used in the color and imaging science fields to take direct, absolute measurements of radiation.
Furthermore, a spectroradiometer samples this radiation at a number of different wavelengths, and thus is able to determine the amount of radiation as a function of the wavelength of light.
Because of these properties, a spectroradiometer is most often used to quantify the direct emission of light from a source.
However, it is also important to note that the instrument can also be used to measure absolute emission from secondary sources such as reflecting or transmitting media.

Spectroradiometers are made with a wide variety of measurement geometries.
However, these devices almost always measure radiation in terms of spectral radiance, which are $Wm^{-2}sr^{-1}nm^{-1}$.
These units discuss the density of energy within a geometric volume between a sample and a detector.
The size of the sample is expressed as a solid angle over which energy is averaged.
Because of this dependency on angle, the spectral radiance measured for a homogeneous sample does not vary on the distance of the device from the sample.

In this lab, a Konika-Minolta CS-1000 spectroradiometer was used to measure a series of light sources.
Four different source measurements were considered during this experiment.
Each source is a different setting in a VeriVide light booth.
This light booth is a tool that provides constant, standard illumination in order to view samples.
It is primarily used for visual matching, but can be useful for providing a set of standard sources.
The VeriVide system uses fluorescent and incandescent lamps to approximate different illuminants.
However, because CIE illuminants are theoretical constructions and not physically reproducable, we describe the lighting conditions provided by the VeriVide light booth as sources.
The four sources available are D65, D50, TL-84, and Illuminant A.
These sources share a name with the CIE illuminants, but are only approximations.


\section{Procedure}


We did not measure the sources in this lab.
Instead, previously collected data was analyzed.
This data was provided by the lab instructor.

As such, the procedure involved using the provided Konika-Minolta software to view and compare the different measured sources in a variety of color spaces.
Then, the data was exported in a CSV format for further processing in other software.
 
Data calculation was performed using the 1nm CIE 1931 color matching functions as published by the Munsell Color Science Lab.
Because of this, numbers may vary slightly from data collected using other means, because the functions were sampled and not integrated for calculation purposes.

\section{Results}

\FloatBarrier

\begin{figure}[h]
\centering
\includegraphics[width=0.6\textwidth]{spec_all_source.eps}
\caption{The spectral curves of the four sources considered for this lab. All four curves have been normalized to equal power.}
\label{fig:spec_all_source}
\end{figure}

Figure \ref{fig:spec_all_source} shows the spectra of each of the four light sources being considered.
While these sources are named after illuminants, they are not exactly the CIE illuminants.
Instead, they are physical realizations that attempt to emulate the CIE standard illuminants.
As a result, the curve shapes do not match the CIE published curves for these illuminants.

In order to compare these plots effectively, each source has been area-normalized.
This means that the relative power of each of the curves is the same.
This is beneficial for comparison, because it means that there is not an overall bias towards one source versus another due to a different overall brightness.

Two comparisons between these spectra are of particular interest.
First, Figure \ref{fig:spec_a_tl84} shows the spectra of the illuminant A emulator and the TL-84 source.
These two curves look so different due to the underlying physics of the light production in each source.
The illuminant A source is an incandescent source.
This means that a piece of metal (usually tungsten) is energized to very high temperatures.
At these states, the piece of metal begins to emit visible radiation.
This radiation is continuous, and the shape can be described by the Plank blackbody curve.

On the other hand, the TL-84 source is a fluorescent source. 
This means that certain gasses are energized in a particular manner.
Even without the gasses being hot enough to emit energy in the visible spectrum as a blackbody radiator, the chemical nature of the gas molecules creates a fluorescent effect.
This effect emits large amounts of radiation, normally within a very small bandwidth.
This can be seen in the very spiky, irregular nature of the source curve.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{spec_a_tl84.eps}
\caption{The TL-84 and A sources compared directly. Both curves have been normalized to equal power.}
\label{fig:spec_a_tl84}
\end{figure}

The second spectral comparison of interest is between the D50 and D65 sources.
As seen in Figure \ref{fig:spec_d50_d65}, these sources are both fluorescent sources.
However, they are designed to emulate two different CIE illuminants.
To do so, different amounts of energy are needed in different parts of the spectrum.
D65 is a ``bluer'' light. As a result, more energy is needed in the short wavelengths than in comparison to D50.
To achieve this, the fluorescent tube manufacturers will adjust the composition of the gas in the tube, or add different phosphorescent coatings to the inside of the tube to improve emission in different parts of the spectrum.
The results of this are evident in the curves.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{spec_d50_d65.eps}
\caption{The D50 and D65 emulators compared directly. Both curves have been normalized to equal power.}
\label{fig:spec_d50_d65}
\end{figure}

Viewing the spectra of each light source can be helpful, but in this case it does not provide a lot of information.
Instead, each source will be transformed into more useful coordinate spaces to investigate the differences between each light.

First, the sources are examined in the x-y chromaticity space (Figure \ref{fig:xy_chromaticity}).
In this space, the relative chroma of each source can be examined.
Additionally, a curve is added, called the Planckian Locus, that shows the chromaticities of blackbody radiators of varying temperatures.
This is often used to examine light sources by comparing the source to the nearest Planckian radiator.
In this case, all four of the sources lie almost directly on the Planckian Locus.
This is an expected behavior for conventional light sources, because these are often percieved as ``natural'' by the human visual sytem.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{xy_chromaticity.eps}
\caption{The x-y chromaticities of each source are plotted. Note that all of the sources fall very close to the Planckian Locus on the diagram.}
\label{fig:xy_chromaticity}
\end{figure}

The x-y chromaticiy space has some drawbacks, however.
Distances between two points in the space do not match the human's perception of these differences.
In other words, the same Euclidian distance does not always mean the same percieved difference by an observer.

To deal with this, the sources are plotted in the $u'$ $v'$ coordinate system.
While this space is not visually uniform either, it does a much better job of presenting information in a way that can be considered visually.
Here, it is apparent that the illuminant A emulator is perceptually very different from the other three.
Again, this is as expected because the incandescent source has a very different observable color to it.

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{uprime_vprime_chromaticity.eps}
\caption{The four sources plotted in the u' v' chromaticity space. This space allows for better comparison of relative distance between the source chromaticities.}
\label{fig:upvp_chromaticity}
\end{figure}

A source's spectrum can be characterized with a color temperature.
The color temperature of a source can only be considered if it resembles a black body radiator.
Our sources plot very near the plankian black body curve and thus, can be considered for color termperature identification.
The color temperature of a source is the temperature of a black body radiator that  that radiates light of comparable hue to that of the light source.
It is denoted in units of Kelvin (K).
Color temperatures over 5,000K are considered ``cool" colors, or bluish in color appearance.
Color temperatures in the 2,700K to 3,000 K range are considered `` warm" colors, or yellowish/redish in color appearance.
Any color temperature between 3,000K and 5,000K are generally perceived as ``white".

Table \ref{tbl:colortemp} shows the calculated color temperatures of each of the source measured as determined by the program used.
It can be seen that illuminant A had the ``warmest" color temperature while illuminant D65 had the ``coolest".
This follows what was observed both in the spectral plots and the chromaticity plots.
The spectra that had more long wavelength energy were ``warmer" while the spectra that had more short wavelength energy were ``cooler".
The $xy$ chromaticity coordinates that plotted closer to the right of the black body curve were ``warmer" than those that plotted further to the left.

\begin{table}[!t]
\caption{Color temperatures of sources according to software.}
\label{tbl:colortemp}
\centering
\begin{tabular}{|c|c|}
\hline
Light Source	&	Correlated Color Temperature (K)	\\ \hline
A               	&	2481	\\ \hline
TL84            	&	3880	\\ \hline
D65             	&	6143	\\ \hline
D50             	&	4827	\\ \hline
\end{tabular}
\end{table}

\FloatBarrier

\section{Conclusions}

In this lab, we examined different light sources, and considered different ways to view, compare, and discuss them.
There is a relationship between the spectral power distribution of a source, the $xy$ chromaticity values, and the color temperature.
We also learned the difference between a source and an illuminant, and when to consider each.
The distributino of the sources energy across the visible spectrum will influence where it will plot in the chromaticity diagram, as well as what color temperature the source will have.
Because there was no hands-on measurement, there is not any way to provide analysis of error, except to say that the results of the experiment match what has been learned in class.

\end{document}
